Let's get one thing straight. From the very beginning, it should be understood that the Tour de Korea is not the Tour de France. But you know what? That is perfectly fine. It is perfectly fine with everyone involved; from the spectators to the organizers to even the competitors. Perfectly fine.
And that is why it is such a great opportunity for everyone in Korea. The Tour de Korea provides the perfect excuse for getting out of wherever you are and seeing the country.
That's not to say the bicycle race will not be exciting. Quite the contrary. These are world-class cyclists busting their butts every day, and it will undoubtedly be quite enjoyable to watch. So you should make plans now to watch the Tour in one of the cities it passes through.
However, it will not require your focus. Don't even worry about having to pretend to care about the race. You don't need to know any of the riders you see. Nobody will care about your ignorance. Instead, just enjoy being in a different location from what you're used to.
Enjoy the local scenery. Enjoy the local food. Enjoy being in a new place. As a side, go ahead and enjoy the race going on. Just enjoy it all.
Few people will be able to follow the Tour de Korea's route from star to finish (Busan to Seoul) over the course of its 8 days. Don't even try. Instead, just pick one place that it is passing through and head there. Make the most of what you can spare.
You can find a brief overview of the tour de Korea's route and schedule below. Each link will take you to the appropriate Wikipedia page. For more information, check out the Tour de Korea's website.
Stage 2: Gumi -> Muju (June 8)
-Gumi is the hometown of former president of South Korea Park Chung-hee and his daughter, current president Park Geun-hye.
-Muju is home to a popular Firefly Festival and a gateway to Mt. Deokyu National Park.
Stage 3: Muju -> Muju (June 9)
-Spend time rafting the Geum River.
Stage 4: Muju -> Yeosu (June 10)
-Check out Mt. Jeoksang while in Muju.
-Yeosu has a lot of history, especially in regards to warfare in Korea.
Stage 6: Gangjin -> Gunsan (June 12)
-Take time to explore Gangjin. It's a beautiful part of the country.
-Gunsan has a fantastic group of islands, the Gunsan Islands, which are worthy of 3 GBs of your digital camera's memory.
Stage 7: Gunsan -> Daejeon (June 13)
-Gunsan is home to a United States Air Force's Kunsan Air Base.
-Daejeon is South Korea's 5th largest metropolis.
Stage 8: Seoul -> Seoul (June 14)
-Seoul should need no introduction.
Enjoy your tour!